Question: Simplify the following expression: $ x = \dfrac{-5}{8} - \dfrac{10n}{n + 10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{n + 10}{n + 10}$ $ \dfrac{-5}{8} \times \dfrac{n + 10}{n + 10} = \dfrac{-5n - 50}{8n + 80} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{10n}{n + 10} \times \dfrac{8}{8} = \dfrac{80n}{8n + 80} $ Therefore $ x = \dfrac{-5n - 50}{8n + 80} - \dfrac{80n}{8n + 80} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-5n - 50 - 80n }{8n + 80} $ Distribute the negative sign: $x = \dfrac{-5n - 50 - 80n}{8n + 80}$ $x = \dfrac{-85n - 50}{8n + 80}$